A Hybrid Direct-Indirect Approach for Solving the Singular Optimal Control Problems of Finite and Infinite Order

Abstract

This paper presents a hybrid approach to solve singular optimal control problems. It combines the direct Euler method with a modified indirect shooting method. The presented method circumvents the main difficulties and drawbacks of both the direct and indirect methods, when applied to the singular optimal control problems. This method does not require a priori knowledge of the switching structure of the solution and it can be applied to finite or infinite order singular optimal control problems. It provides not only an approximate optimal solution for the problem but, remarkably, it also produces the switching times. We illustrate the features of this new approach treating numerically through two optimal control problems, one of finite order and the other with infinite order.